Quantum Gravity coupled to Matter via Noncommutative Geometry

Details Quantum Gravity coupled to Matter via Noncommutative Geometry Quantum Gravity coupled to Matter via Noncommutative Geometry

2010-12-03

arxiv.org/abs/1012.0713v1

Class.Quant.Grav.28:075014,2011

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 1 figure

Scientific paper

10.1088/0264-9381/28/7/075014

We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a configuration space of connections. It involves an algebra of holonomy loops represented as bounded operators on a separable Hilbert space and a Dirac type operator. Semi-classical states, which involve an averaging over points at which the product between loops is defined, are constructed and it is shown that the Dirac Hamiltonian emerges as the expectation value of the Dirac type operator on these states in a semi-classical approximation.

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